Potion

AtCoder

IDabc192_f

Time2000ms

Memory256MB

Difficulty—

There are $N$ kinds of materials. Material $i$ has a magic power of $A_i$. Takahashi, the magician, wants to make a potion by choosing one or more kinds from these materials and mixing them. At the moment when he makes a potion by mixing $k$ kinds of materials, the magic power of the potion is the sum of the materials used. Then, every second, its magic power increases by $k$. Note that the increase of the magic power is a discrete - not continuous - process. Takahashi will mix materials just once, at time $0$. What is the earliest time he can get a potion with a magic power of exactly $X$? Under the constraints, it can be proved that it is possible to make a potion with a magic power of exactly $X$. ## Constraints * $1 \leq N \leq 100$ * $1 \leq A_i \leq 10^7$ * $10^9 \leq X \leq 10^{18}$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $X$ $A_1$ $\ldots$ $A_N$ [samples]

Samples

Input #1

3 9999999999
3 6 8

Output #1

4999999994

The potion made by mixing Material $1$ and Material $3$ has a magic power of $3+8=11$ at time $0$, and it increases by $2$ every second, so it will be $9999999999$ at time $4999999994$, which is the earliest possible time.
The potion made by mixing all the materials $1, 2, 3$ will have a magic power of $9999999998$ at time $3333333327$ and $10000000001$ at time $3333333328$, so it will never be exactly $9999999999$.

Input #2

1 1000000000000000000
1

Output #2

999999999999999999

API Response (JSON)

{
  "problem": {
    "name": "Potion",
    "description": {
      "content": "There are $N$ kinds of materials. Material $i$ has a magic power of $A_i$. Takahashi, the magician, wants to make a potion by choosing one or more kinds from these materials and mixing them. At the mo",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc192_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ kinds of materials. Material $i$ has a magic power of $A_i$.\nTakahashi, the magician, wants to make a potion by choosing one or more kinds from these materials and mixing them.\nAt the mo...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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